Abstract

Phonation onset is characterized by the unstable growth of vocal fold (VF) vibrations that ultimately results in self-sustained oscillation and the production of modal voice. Motivated by histological studies, much research has focused on the role of the layered structure of the vocal folds in influencing phonation onset, wherein the outer “cover” layer is relatively soft and the inner “body” layer is relatively stiff. Recent research, however, suggests that the body-cover (BC) structure over-simplifies actual stiffness distributions by neglecting important spatial variations, such as inferior–superior (IS) and anterior–posterior gradients and smooth transitions in stiffness from one histological layer to another. Herein, we explore sensitivity of phonation onset to stiffness gradients and smoothness. By assuming no a priori stiffness distribution and considering a second-order Taylor series sensitivity analysis of phonation onset pressure with respect to stiffness, we find two general smooth stiffness distributions most strongly influence onset pressure: a smooth stiffness containing aspects of BC differences and IS gradients in the cover, which plays a role in minimizing onset pressure, and uniform increases in stiffness, which raise onset pressure and frequency. While the smooth stiffness change contains aspects qualitatively similar to layered BC distributions used in computational studies, smooth transitions in stiffness result in higher sensitivity of onset pressure than discrete layering. These two general stiffness distributions also provide a simple, low-dimensional, interpretation of how complex variations in VF stiffness affect onset pressure, enabling refined exploration of the effects of stiffness distributions on phonation onset.

References

1.
Suthers
,
R. A.
,
Fitch
,
W. T.
,
Fay
,
R. R.
, and
Popper
,
A. N.
, eds.,
2016
, “
Vertebrate Sound Production and Acoustic Communication
,”
Springer Handbook of Auditory Research
, Vol.
53
,
Springer International Publishing
,
Cham, Switzerland
.
2.
Mittal
,
R.
,
Erath
,
B. D.
, and
Plesniak
,
M. W.
,
2013
, “
Fluid Dynamics of Human Phonation and Speech
,”
Annu. Rev. Fluid Mech.
,
45
(
1
), pp.
437
467
.10.1146/annurev-fluid-011212-140636
3.
Zhang
,
Z.
,
2016
, “
Mechanics of Human Voice Production and Control
,”
J. Acoust. Soc. Am.
,
140
(
4
), pp.
2614
2635
.10.1121/1.4964509
4.
Titze
,
I. R.
,
1988
, “
The Physics of Small–Amplitude Oscillation of the Vocal Folds
,”
J. Acoust. Soc. Am.
,
83
(
4
), pp.
1536
1552
.10.1121/1.395910
5.
Hoffman
,
M. R.
,
Scholp
,
A. J.
,
Hedberg
,
C. D.
,
Lamb
,
J. R.
,
Braden
,
M. N.
,
McMurray
,
J. S.
, and
Jiang
,
J. J.
,
2019
, “
Measurement Reliability of Phonation Threshold Pressure in Pediatric Subjects
,”
Laryngoscope
,
129
(
7
), pp.
1520
1526
.10.1002/lary.27418
6.
Sivasankar
,
M.
, and
Fisher
,
K. V.
,
2002
, “
Oral Breathing Increases Pth and Vocal Effort by Superficial Drying of Vocal Fold Mucosa
,”
J. Voice
,
16
(
2
), pp.
172
181
.10.1016/S0892-1997(02)00087-5
7.
Rousseau
,
B.
,
Sohn
,
J.
,
Tateya
,
I.
,
Montequin
,
D. W.
, and
Bless
,
D. M.
,
2004
, “
Functional Outcomes of Reduced Hyaluronan in Acute Vocal Fold Scar
,”
Ann. Otol. Rhinol. Laryngol.
,
113
(
10
), pp.
767
776
.10.1177/000348940411301001
8.
Zhuang
,
P.
,
Sprecher
,
A. J.
,
Hoffman
,
M. R.
,
Zhang
,
Y.
,
Fourakis
,
M.
,
Jiang
,
J. J.
, and
Wei
,
C. S.
,
2009
, “
Phonation Threshold Flow Measurements in Normal and Pathological Phonation
,”
Laryngoscope
,
119
(
4
), pp.
811
815
.10.1002/lary.20165
9.
Chhetri
,
D. K.
,
Neubauer
,
J.
, and
Berry
,
D. A.
,
2012
, “
Neuromuscular Control of Fundamental Frequency and Glottal Posture at Phonation Onset
,”
J. Acoust. Soc. Am.
,
131
(
2
), pp.
1401
1412
.10.1121/1.3672686
10.
Steinecke
,
I.
, and
Herzel
,
H.
,
1995
, “
Bifurcations in an Asymmetric Vocal–Fold Model
,”
J. Acoust. Soc. Am.
,
97
(
3
), pp.
1874
1884
.10.1121/1.412061
11.
Lucero
,
J. C.
,
1999
, “
A Theoretical Study of the Hysteresis Phenomenon at Vocal Fold Oscillation Onset–Offset
,”
J. Acoust. Soc. Am.
,
105
(
1
), pp.
423
431
.10.1121/1.424572
12.
Strogatz
,
S. H.
,
2018
,
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
, 2nd ed.,
CRC Press
,
Boca Raton, FL
.
13.
Jackson
,
C. P.
,
1987
, “
A Finite-Element Study of the Onset of Vortex Shedding in Flow Past Variously Shaped Bodies
,”
J. Fluid Mech.
,
182
(
1
), pp.
23
45
.10.1017/S0022112087002234
14.
Bryant
,
M.
, and
Garcia
,
E.
,
2011
, “
Modeling and Testing of a Novel Aeroelastic Flutter Energy Harvester
,”
ASME J. Vib. Acoust.
,
133
(
1
), p.
011010
.10.1115/1.4002788
15.
Hirano
,
M.
,
Kakita
,
Y.
,
Ohmaru
,
K.
, and
Kurita
,
S.
,
1982
, “
Structure and Mechanical Properties of the Vocal Fold
,”
Speech and Language
, 1st ed., Vol.
7
,
N. J.
Lass
, ed.,
Elsevier
,
Amsterdam, The Netherlands
, pp.
271
297
.10.1016/B978-0-12-608607-2.50015-7
16.
Hirano
,
M.
,
1974
, “
Morphological Structure of the Vocal Cord as a Vibrator and Its Variations
,”
Folia Phoniatr. Logop.
,
26
(
2
), pp.
89
94
.10.1159/000263771
17.
Hirano
,
M.
, and
Kakita
,
Y.
,
1985
, “
Cover-Body Theory of Vocal Fold Vibration
,”
Speech Science: Recent Advances
,
R.
Daniloff
, ed.,
College-Hill Press
,
San Diego, CA
, pp.
1
46
.
18.
Ishizaka
,
K.
, and
Matsudaira
,
M.
,
1972
,
Fluid Mechanical Considerations of Vocal Cord Vibration, SCRL-Monograph
,
Speech Communication Research Laboratory
,
Santa Barbara, CA
.
19.
Ishizaka
,
K.
, and
Flanagan
,
J. L.
,
1972
, “
Synthesis of Voiced Sounds From a Two-Mass Model of the Vocal Cords
,”
Bell Syst. Tech. J.
,
51
(
6
), pp.
1233
1268
.10.1002/j.1538-7305.1972.tb02651.x
20.
Lucero
,
J. C.
,
1996
, “
Relation Between the Phonation Threshold Pressure and the Prephonatory Glottal Width in a Rectangular Glottis
,”
J. Acoust. Soc. Am.
,
100
(
4
), pp.
2551
2554
.10.1121/1.417365
21.
Lucero
,
J. C.
,
1998
, “
Optimal Glottal Configuration for Ease of Phonation
,”
J. Voice
,
12
(
2
), pp.
151
158
.10.1016/S0892-1997(98)80034-9
22.
Zhang
,
Z.
,
Neubauer
,
J.
, and
Berry
,
D. A.
,
2007
, “
Physical Mechanisms of Phonation Onset: A Linear Stability Analysis of an Aeroelastic Continuum Model of Phonation
,”
J. Acoust. Soc. Am.
,
122
(
4
), pp.
2279
2295
.10.1121/1.2773949
23.
Zhang
,
Z.
,
2009
, “
Characteristics of Phonation Onset in a Two-Layer Vocal Fold Model
,”
J. Acoust. Soc. Am.
,
125
(
2
), pp.
1091
1102
.10.1121/1.3050285
24.
Zhang
,
Z.
, and
Neubauer
,
J.
,
2010
, “
On the Acoustical Relevance of Supraglottal Flow Structures to Low-Frequency Voice Production
,”
J. Acoust. Soc. Am.
,
128
(
6
), pp.
EL378
EL383
.10.1121/1.3515838
25.
Kelleher
,
J. E.
,
Siegmund
,
T. H.
, and
Chan
,
R. W.
,
2012
, “
Could Spatial Heterogeneity in Human Vocal Fold Elastic Properties Improve the Quality of Phonation?
,”
Ann. Biomed. Eng.
,
40
(
12
), pp.
2708
2718
.10.1007/s10439-012-0609-1
26.
Chhetri
,
D. K.
,
Zhang
,
Z.
, and
Neubauer
,
J.
,
2011
, “
Measurement of Young's Modulus of Vocal Folds by Indentation
,”
J. Voice
,
25
(
1
), pp.
1
7
.10.1016/j.jvoice.2009.09.005
27.
Chhetri
,
D. K.
, and
Rafizadeh
,
S.
,
2014
, “
Young's Modulus of Canine Vocal Fold Cover Layers
,”
J. Voice
,
28
(
4
), pp.
406
410
.10.1016/j.jvoice.2013.12.003
28.
Geng
,
B.
,
Xue
,
Q.
, and
Zheng
,
X.
,
2016
, “
The Effect of Vocal Fold Vertical Stiffness Variation on Voice Production
,”
J. Acoust. Soc. Am.
,
140
(
4
), pp.
2856
2866
.10.1121/1.4964508
29.
Farbos de Luzan
,
C.
,
Maddox
,
A.
,
Oren
,
L.
,
Gutmark
,
E.
,
Howell
,
R. J.
, and
Khosla
,
S. M.
,
2021
, “
Impact of Vertical Stiffness Gradient on the Maximum Divergence Angle
,”
Laryngoscope
,
131
(
6
), pp.
E1934
E1940
.10.1002/lary.29345
30.
Benboujja
,
F.
, and
Hartnick
,
C.
,
2021
, “
Quantitative Evaluation of the Human Vocal Fold Extracellular Matrix Using Multiphoton Microscopy and Optical Coherence Tomography
,”
Sci. Rep.
,
11
(
1
), p.
2440
.10.1038/s41598-021-82157-9
31.
Zhang
,
Z.
,
2010
, “
Dependence of Phonation Threshold Pressure and Frequency on Vocal Fold Geometry and Biomechanics
,”
J. Acoust. Soc. Am.
,
127
(
4
), pp.
2554
2562
.10.1121/1.3308410
32.
Alipour
,
F.
,
Berry
,
D. A.
, and
Titze
,
I. R.
,
2000
, “
A Finite-Element Model of Vocal-Fold Vibration
,”
J. Acoust. Soc. Am.
,
108
(
6
), pp.
3003
3012
.10.1121/1.1324678
33.
Movahhedi
,
M.
,
Geng
,
B.
,
Xue
,
Q.
, and
Zheng
,
X.
,
2021
, “
Effects of Cricothyroid and Thyroarytenoid Interaction on Voice Control: Muscle Activity, Vocal Fold Biomechanics, Flow, and Acoustics
,”
J. Acoust. Soc. Am.
,
150
(
1
), pp.
29
42
.10.1121/10.0005275
34.
Hadwin
,
P. J.
,
Motie-Shirazi
,
M.
,
Erath
,
B. D.
, and
Peterson
,
S. D.
,
2019
, “
Bayesian Inference of Vocal Fold Material Properties From Glottal Area Waveforms Using a 2D Finite Element Model
,”
Appl. Sci.
,
9
(
13
), p.
2735
.10.3390/app9132735
35.
Scherer
,
R. C.
,
Shinwari
,
D.
,
De Witt
,
K. J.
,
Zhang
,
C.
,
Kucinschi
,
B. R.
, and
Afjeh
,
A. A.
,
2001
, “
Intraglottal Pressure Profiles for a Symmetric and Oblique Glottis With a Divergence Angle of 10 Degrees
,”
J. Acoust. Soc. Am.
,
109
(
4
), pp.
1616
1630
.10.1121/1.1333420
36.
Bathe
,
K. J.
,
2006
,
Finite Element Procedures
, 2nd ed.,
Klaus-Jürgen Bathe
,
Watertown, MA
.
37.
Fung
,
Y.-C.
,
1993
,
Biomechanics
, 2nd ed.,
Springer
,
New York
.
38.
Zheng
,
X.
,
Bielamowicz
,
S. A.
,
Luo
,
H.
, and
Mittal
,
R.
,
2009
, “
A Computational Study of the Effect of False Vocal Folds on Glottal Flow and Vocal Fold Vibration During Phonation
,”
Ann. Biomed. Eng.
,
37
(
3
), pp.
625
642
.10.1007/s10439-008-9630-9
39.
Logg
,
A.
,
Kent-Andre
,
M.
, and
Wells
,
G. N.
,
2012
,
Automated Solution of Differential Equations by the Finite Element Method (Lecture Notes in Computational Science and Engineering)
, Vol.
84
,
Springer
,
Berlin, Heidelberg
.
40.
Logg
,
A.
, and
Wells
,
G. N.
,
2010
, “
DOLFIN: Automated finite element computing
,”
ACM Trans. Math. Software
,
37
(
2
), pp.
1
28
.10.1145/1731022.1731030
41.
Phillips
,
R.
,
Zhang
,
Y.
,
Keuler
,
M.
,
Tao
,
C.
, and
Jiang
,
J. J.
,
2009
, “
Measurement of Liquid and Solid Component Parameters in Canine Vocal Fold Lamina Propria
,”
J. Acoust. Soc. Am.
,
125
(
4
), pp.
2282
2287
.10.1121/1.3086276
42.
Griewank
,
A.
, and
Reddien
,
G.
,
1983
, “
The Calculation of Hopf Points by a Direct Method
,”
IMA J. Numer. Anal.
,
3
(
3
), pp.
295
303
.10.1093/imanum/3.3.295
43.
Boullé
,
N.
,
Farrell
,
P. E.
, and
Rognes
,
M. E.
,
2022
, “Optimization of Hopf Bifurcation Points,”
SIAM J. Sci. Comput.
, 45(3), pp. B390–B411.10.1137/22M1474448
44.
Hamby
,
D. M.
,
1994
, “
A Review of Techniques for Parameter Sensitivity
,”
Environ. Monit. Assess.
,
32
(
2
), pp.
135
154
.10.1007/BF00547132
45.
Hernandez
,
V.
,
Roman
,
J. E.
, and
Vidal
,
V.
,
2005
, “
SLEPC: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems
,”
ACM Trans. Math. Software
,
31
(
3
), pp.
351
362
.10.1145/1089014.1089019
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